What are the consequences for this breakage? The article says current models do not easily fit the asymmetry but does not state what parts of our understanding will break if those models are wrong.
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So I expect in this cases the guesses were wrong and the Standard Model will manage to explain that as well.
In its current agreed upon form it's just SU(3)xSU(2)xU(1). This gauge symmetry defines the lagrangian, which has 19 parameters to be determined by experiment.
It's true that this isn't the whole story (dark matter etc), but these symmetries are physically motivated and their predictive power is pretty amazing (the QED part is CORRECT as far as any experiment has been able to check so far).